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A051470
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a(n) is least value of m for which the sum of Liouville's function from 1 to m is n.
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9
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1, 906150258, 906150259, 906150260, 906150263, 906150264, 906150331, 906150334, 906150337, 906150338, 906150339, 906150358, 906150359, 906150362, 906150363, 906150368, 906150387, 906150388, 906150389, 906150406, 906150407
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| It was once conjectured that the sum of Liouville's function was never > 0 except for the first term.
It follows from Theorem 2 in Borwein-Ferguson-Mossinghoff that a(n) < 262*n^2 infinitely often, improving on an earlier result of Anderson & Stark. [Charles R Greathouse IV, Jun 14 2011]
a(830) > 2 * 10^14 (probably around 3.511e14) and a(1160327) = 351753358289465 according to the calculations of Borwein, Ferguson, & Mossinghoff. [Charles R Greathouse IV, Jun 14 2011]
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REFERENCES
| R. S. Lehman, On Liouville's function, Mathematics of Computation 14 (1960), pp. 311-320.
M. Tanaka, A numerical investigation on cumulative sum of the Liouville function, Tokyo Journal of Mathematics 3 (1980), pp. 187-189.
R. J. Anderson and H. M. Stark, Oscillation theorems, Analytic Number Theory (1980); Lecture Notes in Mathematics 899 (1981), pp. 79-106.
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LINKS
| Donovan Johnson, Table of n, a(n) for n = 1..829
P. Borwein, R. Ferguson, and M. Mossinghoff, Sign changes in sums of the Liouville function, Mathematics of Computation 77 (2008), pp. 1681-1694.
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EXAMPLE
| The sum of Liouville's function from 1 through 906150258 is 2, that is the smallest value, so a(2)=906150258.
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PROG
| (PARI) print1(r=1); t=0; for(n=906150257, 906400000, t+=(-1)^bigomega(n); if(t>r, r=t; print1(", "n))) /* Charles R Greathouse IV, Jun 14 2011 */
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CROSSREFS
| Sequence in context: A178557 A157798 A189229 * A076135 A015382 A115385
Adjacent sequences: A051467 A051468 A051469 * A051471 A051472 A051473
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KEYWORD
| nonn
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AUTHOR
| Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu)
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